Resumen:
In this dissertation, we will adress recent developments in the theory of topological cardinal invariants, as well as their motivations from classical results. We will
introduce the elementary submodels, a tool that is widely used in the proof of recent theorems, and we intend to use them not only to prove these, but also to provide alternative
proofs of classical results, such as the bounds on the cardinality of topological spaces by
Arhangel'skii and by Hajnal and Juhász. We are also going to show how some in nite
games can be employed to de ne topological properties that provide partial answers to
Arhangel'skii's question about the cardinality of Lindelöf spaces with points Gδ.
